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Computational aspects of growth-induced instabilities with application to biofilms

Biofilms, similar to other living materials, have the ability to grow and adapt in favor of their surroundings.
The growth of biofilms is often due to the secretion of extracellular polymeric substances (EPS) produced by micro-organisms.
Biofilm growth can form wrinkling or other more complicated folding patterns, overall referred to as growth-induced instabilities, depending on the specific geometry and the boundary conditions of the problem.

The continuum mechanical treatment of this process proves to be a powerful tool to provide deeper insights into the mechanics of the biofilm growth.
The continuum mechanics model simplifies the problem as a thin film growing on a soft infinite substrate where the folding formation with a characteristic wavelength starts when the growth reaches a critical value.
Although the continuum model is relatively straightforward through a multiplicative decomposition of the deformation gradient into its elastic and growth parts, the numerical aspects of the problem seem to be very challenging due to the nature of the instability analysis.

The objective of this presentation is to establish a computational framework based on the finite element method to capture growth-induced instabilities.
This study details different methods as well as different finite element types.
The results are compared against the analytical solutions for simple problems with available analytical solutions, and it is observed that eigenvalue analysis provides the most accurate and reliable results.
Nevertheless, a careful perturbation analysis could also provide satisfactory results if the elements are chosen properly and the perturbation is applied correctly.
In addition, various parameters such as biofilm thickness, growth rate, and elasticity modulus ratio of biofilm to the substrate affect the onset of the instability and the wavelength of the biofilm.
These findings demonstrate the importance of a correct and reliable numerical scheme.

Author(s):

Berkin Dortdivanlioglu    
Stanford University, Department of Civil and Environmental Engineering
United States

Ali Javili    
Stanford University, Department of Civil and Environmental Engineering
United States

Christian Linder    
Stanford University, Department of Civil and Environmental Engineering
United States